Electric current is given by:
i = i₀(t/T)
for 0 ≤ t ≤ T. Find the RMS current.

Question

Electric current is given by:
i = i₀(t/T)
for 0 &le; t &le; T. Find the RMS current.

Shiksha Nation · Accepted Answer

Solution:
RMS current:
Irms = &radic;[(1/T)&int;i&sup2;dt]
Substituting:
Irms = &radic;[(1/T) &int;₀ᵀ (i₀&sup2;t&sup2;/T&sup2;)dt]
= (i₀/T) &radic;[(1/T) &int;₀ᵀ t&sup2;dt]
= (i₀/T) &radic;[(1/T)(T&sup3;/3)]
= (i₀/T) &radic;(T&sup2;/3)
= i₀/&radic;3
Answer: i₀/&radic;3

Electric current is given by: i = i₀(t/T) for 0 ≤ t ≤ T. Find the RMS current.

Verified Answer

Electric current is given by:

i = i₀(t/T)

for 0 ≤ t ≤ T. Find the RMS current.